When Thor loses his hammer, he believes he is no longer as strong as he was because he lost his powers as the God Of Thunder.

Odin comes to him in a vision (twice) and shows that the hammer "was to focus his power". We first see that Thor has the powers of thunder within him when he was being battered by Hulk.

When Hela was about to kill him and asked him "What are you the God of?" Odin came to him and told him he has the powers of the hammer inside him.

If this is the case does he lose certain powers because he no longer has it with him physically?

For example:

At the start of the film Thor is seen placing the hammer on the jaw of the dragon and causing it to be locked down on the ground because as we already know 'those who are worthy can only posses the powers of Thor'.

Thor has been seen before at other times placing the hammer on villains to stop them from moving.

Without his hammer how will he do this? Or does he lose this power?

Another power he had was to control his hammer psychologically, for example when in the Sanctum Sanctorium he calls for the hammer and it travels to him (while smashing a few stuff) and he has the power to stop the velocity of the hammer mid-air for example when fighting Surturs minions the hammer is seen flying in circles then decelerating and returning to his palm at command.

The hammer is a device, not a power. If someone loses a gun, there was no "fire bullets" power they had that they've now lost. That said, it was confirmed in the film that his flight was essentially him twirling and throwing his hammer while holding it. Inability to fly seemed to have been confirmed when he needed Hulk to get him and Valkrie onto the departing ship.
– sirjonsnowNov 7 '17 at 14:35

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@sirjonsnow actually i believe he can fly because after hitting Hela with a thunder bolt he flies down to the bridge I think Hulk and Valkyrie carried him because he was injured
– Metro BoominNov 7 '17 at 16:13

That could be; I almost mentioned he was kind of "floaty" during the final battle, but we never see him zooming around either.
– sirjonsnowNov 7 '17 at 16:17

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Don't forget that after being told not to Fight, Hulk basically made the decision to carry them without asking. Thor may well have been able to fly on his own but not had the chance as Hulk immediately grabbed him after being told not to fight.
– IronSeanNov 20 '17 at 14:41

2 Answers
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It's pretty obvious that Thor can't do all the stuff that you mentioned simply because the hammer is not there anymore. However, he is still able to fly as we have seen in the movie. The "powers of the hammer" that Odin is referring to is, whatever things that Thor have done till now with the hammer, he will be able to do that without it.

Placing the hammer somewhere and Thor is the only one who can lift it doesn't considered as a power (even though it's pretty cool) it's mere a ability. The power that Odin mentions is mainly about the physical ability the hammer posses and the ability to bring in the thunder. But as we have seen in the movie, Thor does't need the hammer to bring in the thunder, it was just a tool that was used to shape his power and controlling it.

These are innate to all Asgardians I believe (even if many are not as strong as Thor in particular). These also don't leave when Thor was without his hammer in Ragnarok, though they do seem diminished in the original Thor movie.

The Powers of Thor

Fly

Control Lightning

There are Thor's Godlike powers. He seemed to lose them without the hammer to focus them before, but those are actually powers innate to Thor and come from himself/the people of Asgard.

The Abilities of Mjolnir

Unmovable weight unless lifted by someone worthy

Ability to be controlled and summoned by Thor

I think these are traits imbued on the hammer itself, the weight one specifically as a test for Thor in the first Thor movie. They are not a power of Thor but instead a property of Mjolnir and Odin's magic. They are no longer usable with the hammer destroyed.